Problem: Simplify the expression. $(4a^{4}-6a^{3}+a^{2})(3a^{2}+2a)$
Solution: First use the distributive property. $ 4 a^4 (3 a^2) + 4 a^4 (2 a) - 6 a^3 (3 a^2) - 6 a^3 (2 a) + a^2 (3 a^2) + a^2 (2 a) $ Simplify. $ 12a^{6} + 8a^{5} - 18a^{5} - 12a^{4} + 3a^{4} + 2a^{3} $ $12a^{6}-10a^{5}-9a^{4}+2a^{3}$ Identify like terms. $ { 12a^{6}} \color{#DF0030} {+ 8a^{5}} \color{#DF0030} {- 18a^{5}} {- 12a^{4}} {+ 3a^{4}} {+ 2a^{3}} $ Add the coefficients. $ { 12a^{6}} \color{#DF0030} { -10a^{5}} { -9a^{4}} {+ 2a^{3}} $